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Unformatted text preview: Problem Set II Corporate Finance MSF 534 Due Sep 17, 2009 Problem 1. One can run a time-series regression r it = i + i r mt + it to obtain an estimate of i and its standard error. The estimation result also give a risk decomposition of the security. The following table shows estimates for two well-known British stocks during the five years ending July 2001: Stock i Standard Deviation of return r i R 2 i estimate Standard Error of i British Petroleum (BP) 25 0.25 0.9 0.17 British Airways 38 0.25 1.37 0.22 [Hint: page 244 of your text (9th edition) is helpful.] a. What proportion of each stocks risk was market risk, and what proportion was unique risk? Ans. Both British Petroleum and British Airways had R 2 values of 0.25, which means that, for both stocks 25% of total risk comes from movements in the market (i.e., market risk). Therefore, 75% of total risk is unique risk. b. What is the variance of BP? What is the unique variance? Ans. The variance of British Petroleum is (25) 2 = 625 Unique variance for British Petroleum is: (0 . 75 625) = 468 . 75 c. What is the confidence level on British Airways beta? Ans. The t-statistic for BA is (0 . 90 / . 17) = 5 . 29 This is significant at the 1% level, so that the confidence level is 99%. d. If the CAPM is correct, what is the expected return on British Airways? Assume a risk-free interest rate of 5 percent and an expected market return of 12 percent. Ans. r BP = r f ( r m- r f ) = 0 . 05 + 1 . 37 (0 . 12- . 05) = 0 . 145 9 e. Suppose that next year the market provides a zero return. What return would you expect from British Airways? Ans. r BP = r f ( r m- r f ) = 0 . 05 + 1 . 37 (0- . 05) =- . 018 5 Problem 2 . Amalgamated Products has three operating divisions: Division Percentage of Firm Value Food 50 Electronics 30 Chemicals 20 1 To estimate the cost of capital for each division, Amalgamated has identified the following three principal competitors: Estimated Equity Beta Debt/(Debt + Equity) United Foods 0.8 0.3 General Electronics 1.6 0.2 Associated Chemicals 1.2 0.4 Assume these betas are accurate estimates and that the CAPM is correct. a. Assuming that the debt of these firms is risk-free, estimate the asset beta for each of Amalgamateds divisions. Ans. With risk-free debt, asset = E/V equity . Therefore food = 0 . 7 . 8 = 0 . 56 elec = 0 . 8 1 . 6 = 1 . 28 chem = 0 . 6 1 . 2 = 0 . 72 b. Amalgamateds ratio of debt to debt plus equity is .4. If your estimates of divisional betas are right, what is Amalgamateds equity beta? Ans. assets = (0 . 5 . 56) + (0 . 3 1 . 28) + (0 . 2 . 72) = 0 . 808 Still assuming risk-free debt: asset = E/V equity . 81 = (0 . 6) equity equity = 1 . 35 c. Assume that the risk-free interest rate is 7 percent and that the expected return on the market index is 15 percent. Estimate the cost of capital for each of Amalgamateds divisions....
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